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integration of dx/√-log x=√π with limits 0 to 1 please solve it immediately

integration of dx/√-log x=√π with limits 0 to 1
please solve it immediately
 

Grade:12th pass

2 Answers

Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
check your question once you have written nregative inside root is it there??
jagdish singh singh
173 Points
3 years ago
\hspace{-0.75 cm}$ Let $I = \int^{1}_{0}\frac{1}{\sqrt{-\ln x}}dx\;,$ nPut $-\ln (x)=t^2$\\\\ and $x=e^{-t^2},$ Then $dx = -2te^{-t^2}dt$ and changing limits\\\\ So $I = 2\int^{\infty}_{0}e^{-t^2}dt = 2\cdot \frac{\sqrt{\pi}}{2} = \sqrt{\pi}.$\\\\ It is well known gaussian Integral or Error function.

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